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We believe a 1903 Immigration and Naturalization Service form may be in Record Group 85 - Records of the Immigration and Naturalization Service, 1787 - 2004. Please contact the National Archives at DC to request a search of the physical holdings for the form.
Please note that due to local COVID-19 guidelines, the staff may have limited access to the facility at this time.
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The National Archives and Records Administration
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To add to what my colleague wrote you may also want to contact the U.S. Citizenship and Immigration Services (USCIS) Historical Library about this form. You can reach them by visiting this link:
They might not be able to provide you a copy of the form but they may be able to provide you with more information on it.
We hope this information is helpful and best of luck with your research!